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arXiv · 2606.24936

A Matrix-Based Polyalphabetic Algorithm for Information Encoding and Decoding Using Number Sequences

Muhammet Karagöz·Nihal Özgür
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Abstract

In this paper, we propose a matrix-based polyalphabetic data encoding and decoding scheme using Fibonacci, Leonardo, Jacobsthal, and Lucas sequences. The method employs three sequence-based alphabets for character substitution and a Lucas-based auxiliary alphabet for word separators. A position-dependent selector, \[ σ=\bigl(v^2+(i-1)+(j-1)\bigr)\pmod 3, \] distributes repeated plaintext symbols among different numerical alphabets, thereby reducing frequency concentration. The resulting numerical matrix is divided into $3\times 3$ blocks and transformed using powers of the Leonardo $Q$-matrix with block-dependent keys generated from pre-shared parameters $(s,p)$. A collision-free public prime $P$ is used to keep ciphertext entries bounded while preserving unique decoding. A worked example and preliminary statistical, entropy, avalanche, and timing results indicate that the proposed modular construction is computationally efficient and provides improved distributional behavior compared with standard monoalphabetic substitution.

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Muhammet Karagöz, Nihal Özgür. 2026-06-22. A Matrix-Based Polyalphabetic Algorithm for Information Encoding and Decoding Using Number Sequences. https://arxiv.org/abs/2606.24936

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